Right local time of a continuous semimartingale ($L_t^{a,+}=|X_t-a|-|X_0-a|-{\int }_0^t(1_{\{X_s>a\}}-1_{\{X_s\le a\}})d{X}_s$)

This normalization uses the left derivative of absolute value in the Tanaka formula. Its increasing correction is the right-sided spatial local time; equivalently $(X_t-a{)}^{+}=(X_0-a{)}^{+}+{\int }_0^t{1}_{\{X_s>a\}}d{X}_s+\frac{1}{2}{L}_t^{a,+}$. It need not equal symmetric local time for a general continuous semimartingale with finite-variation mass at the level. In the smooth convex approximation proof of the Tanaka formula, the second derivatives are supported on the positive side of the level, agreeing with this convention.